A possible solution to the helium anomaly of EMPRESS VIII by cuscuton gravity theory

Abstract We discuss cosmology based on the cuscuton gravity theory to resolve anomaly of observational 4He abundance reported by EMPRESS collaboration. find that gravitational constant Gcos in Friedmann equation should be smaller than Newton’s GN such ${\Delta G_{\rm N}}/{G_{\rm N}} \equiv (G_{\rm cos}-G_{\rm N})/{G_{\rm = -0.085_{-0.028}^{+0.026} \ (68 \% \text{ C.L.})$ terms big-bang nucleosynthesis, which excludes ?GN 0 at more 95% C.L. To fit data, we obtain a negative mass squared non-dynamical scalar field with Planck-mass scale as $\sim - {\mathcal {O}}(1) {M_{\rm PL}^2} ({\mu }/{0.5 M_{\rm PL}})^{4}$ parameter ?. This fact could suggest need for modified theories quadratic potential, can regarded low-energy Ho?ava–Lifshitz gravity, and might give hint quantum gravity.